Optimal communications filters for multirate applications

The author describes optimal communications filters used for multirate applications. The closed-form solution is presented for the lowpass filtering problem where the passband is constrained to be maximally flat and the stopband energy is minimized. The optimal filter is shown to exist for specific passband constraints which are related to a matrix of the Vandermonde type. The relationship between filters of similar design with one or two passband constraints is described. Several design examples are included to demonstrate the effectiveness of the design technique